I have a PS3 with six games, so far.
Assassin's Creed - This is an all around amazing game. Basically, this is a middle ages version of the GTA series, except that you're a good guy, so killing civilians is discouraged. The story gets too unrealistic near the end and was hard for me to follow without subtitles (my only major complaints), but this is definitely a fun game to play. I would have liked more weapons and more fighting techniques, but the playability of this game overall is still phenomenal. Even if you're not that interested in completing the missions, it's still a fun game to play if not simply because of how innovative it is. The movements are based on parkour and free running, so when they say you can climb anything, they really mean ANYTHING. You can climb every building, walk across every rail, skip across every peg, and hang from every crack, crevice or window sill. This game also looks very next-gen, which I'm sure is important to some of you. I really hope someone releases a similar game, but with Ninjas and Samurai (and more weapons, better combat, and several more stealth kill variations [preferably different executions with different weapons]).
GTA4 - The characters and voice acting are better than in any previous GTA game, in my opinion. The new vehicle controls took me a few hours to get used to, but now I actually prefer them over the old style. The cell phone is a welcome addition to the game, but I hate it when I get an unsolicited call and automatically accept a mission that I'm not prepared for. Niko also needs to stop calling people back while on the run, because I've been arrested like three times because he was an idiot and stopped running away from the police to make a phone call and tell someone that he completed an assignment. Also, I can't even express how much I appreciate the GPS directional system.
Gundam: Crossfire - The modile suits aren't truly customizable like in the Armored Core series, instead requiring you to buy upgrades that will improve your stats, and maybe grant access to new weapons. However, each upgrade takes a full (in game) day to complete and you can't perform missions while your MS is receiving maintenance. The missions are still entertaining though. I thought this game was quite difficult at first, but then I figured out how to lock on to targets (I'm a bit ashamed of how long it took me to figure this out), so I started over from the beginning and everything was a breeze. I really enjoy the lobby music, but the graphics are very PS2.
Heavenly Sword - This is the most overrated game since Fighter Maker. The controls are mindnumbingly simple and redundant. You can unlock additional abilities, but they will ultimately do nothing to releave your boredom, as you will still have to continue on with the button-mash-fest in order to power up your special abilities meter. The characters in this game range from stereotypical to completely out of place. The main character is an Angelina Jolie parody, except with an English accent and flowing red hair, but she is supposedly Japanese. The secondary character is an emotionally disturbed walking cliche, but with the redeeming quality that her missions are actually fun. She has a revolver-crossbow and you can hold the fire button to slow down time and steer her arrows. The after touch is complete shit, but if you turn it off, the analogue stick works just fine. The villains look like the freaks of Xerxes' army from the movie 300, but even more unbelievable and annoying. Actually, the lead villain is the only decent, somewhat realistic character in the entire game. The environments however, are out of this world. What this game lacks in playability (everything) it makes up for with the most beautiful scenery of any game I've ever seen and one of my favorite videogame soundtracks to date. Also, the character rendering is phenomenal, although a bit of a waste considering the circumstances.
Turok - This really doesn't stand out from any other first person shooter that I've played. There are some cool weapons and the knife executions are pretty neat, but I've never been much of an FPS fan. I do appreciate however, that the makers of this game put forth a decent effort to ensure that the dinosaurs were represented in an anatomically authentic manner. The Dilophosaurus is full-size, bare-necked and non-acid-spitting, unlike the unrealistic portrayal in Jurassic Park and the raptors actually have feathers, although not as much so as they probably did in real life. Also, this isn't relevant to the PS3 Turok, but in Turok: Evolution (PS2) they chose a Quetzalcoatlus as the official mode of arial transportation, rather than settling to enlarge a Pterodactyl or Pteranodon.
Virtua Fighter 5 - I haven't spent much time with this game yet. So far all I've done is check out all the throws and grapples for each character in the training room, and while those are a lot of fun to watch, I'm not as impressed with this game so far as I have been with the Tekken series. I'm sure I could get used to the controls, but I don't like how the movements are still so punctuated and computerized, even on a next gen console. I much prefer the fluidity of Tekken combat.
I've played a few of the Armored Core games on PS2, so I can't wait to get Armored Core 4, and I'm definitely looking forward to Tekken 6 as well.